In this paper, we revisit the standard Fourier transform in a manner that is consistent with the \(\kappa \) -algebra and the \(\kappa \) -calculus derived in the framework of the \(\kappa \) -statistical mechanics. This formalism, together with the \(\kappa \) -entropy, has been introduced in [1]} to generalize the Boltzmann-Gibbs entropy and the related theory, with the aim to describe non Gibbsian systems characterized by power-law distributions. In the last decade, several papers have been written on the \(\kappa \) -statistical mechanics concerning its foundations, its theoretical consistence and its possible applications to physical and physical-like systems [2]}, [3]}, [4]}, [5]}, [6]}, [7]} (see [8]} for an up to date references list).
